%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO437^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:47:41 AM UTC 2026
% Result : Theorem 0.23s 0.31s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 18
% Syntax : Number of formulae : 193 ( 87 unt; 0 typ; 6 def)
% Number of atoms : 1533 ( 297 equ; 0 cnn)
% Maximal formula atoms : 17 ( 7 avg)
% Number of connectives : 2016 ( 342 ~; 389 |; 13 &;1184 @)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 148 ( 148 >; 0 *; 0 +; 0 <<)
% Number of symbols : 65 ( 61 usr; 12 con; 0-4 aty)
% ( 70 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 350 ( 0 sgn 79 !; 0 ?; 350 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
rel_s4: $i > $i > $o ).
thf(func_def_33,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
q: $i > $o ).
thf(func_def_37,type,
r: $i > $o ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vIMP: $o > $o > $o ).
thf(func_def_44,type,
vAND: $o > $o > $o ).
thf(func_def_45,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vOR: $o > $o > $o ).
thf(func_def_49,type,
vNOT: $o > $o ).
thf(func_def_50,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_51,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_52,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_54,type,
sK1: $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) )
= mand ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) )
= mequiv ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f34,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',a1) ).
thf(f35,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',a2) ).
thf(f36,conjecture,
mvalid @ ( mimplies @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ r ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mbox_s4 @ r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f37,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ r ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mbox_s4 @ r ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f41,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f42,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f43,plain,
~ ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ r ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mbox_s4 @ r ) ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f44,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ r ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mbox_s4 @ r ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f43]) ).
thf(f52,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f59,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f60,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f59]) ).
thf(f65,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f66,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f65]) ).
thf(f67,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f68,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f67]) ).
thf(f73,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f74,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f73]) ).
thf(f76,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f80,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f87,plain,
mtransitive @ rel_s4,
inference(rectify,[],[f35]) ).
thf(f88,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f87]) ).
thf(f93,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f94,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f93]) ).
thf(f95,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f96,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f95]) ).
thf(f98,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ r ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mbox_s4 @ r ) ) ) ) )
!= $true ),
inference(flattening,[],[f44]) ).
thf(f99,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f108,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f110,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f111,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f114,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f88]) ).
thf(f115,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f80]) ).
thf(f117,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f60]) ).
thf(f118,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f96]) ).
thf(f120,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f76]) ).
thf(f123,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f129,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ r ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mbox_s4 @ r ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f132,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f94]) ).
thf(f137,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f123,f111,f132,f111,f111]) ).
thf(f138,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f120,f132,f111]) ).
thf(f140,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f115,f137,f138,f138]) ).
thf(f147,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ rel_s4 )
= $true ),
inference(definition_unfolding,[],[f114,f108]) ).
thf(f148,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f117,f99]) ).
thf(f149,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ p
@ q ) )
@ r ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ p
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ r ) ) ) ) ) ),
inference(definition_unfolding,[],[f129,f118,f138,f110,f138,f110,f140,f110,f138,f110,f140,f110]) ).
thf(f150,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ~ ( ~ ( p @ Y2 )
| ( q @ Y2 ) )
| ~ ( ~ ( q @ Y2 )
| ( p @ Y2 ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( r @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ~ ( ~ ( p @ Y2 )
| ( q @ Y2 ) )
| ~ ( ~ ( q @ Y2 )
| ( p @ Y2 ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( r @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ~ ( ~ ( p @ Y2 )
| ( q @ Y2 ) )
| ~ ( ~ ( q @ Y2 )
| ( p @ Y2 ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( r @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ~ ( ~ ( p @ Y2 )
| ( q @ Y2 ) )
| ~ ( ~ ( q @ Y2 )
| ( p @ Y2 ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( r @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( r @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( r @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f155,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( r @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( r @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) ) )
| ( r @ X1 )
| ~ ( rel_s4 @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) ) )
| ( r @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) ) )
| ( r @ X1 ) ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) )
| ( $true
= ( r @ X1 ) ) ),
inference(not_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) )
@ ( sK1 @ X1 ) ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( r @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X1: $i] :
( ( $false
= ( ~ ( ~ ( ~ ( p @ ( sK1 @ X1 ) )
| ( q @ ( sK1 @ X1 ) ) )
| ~ ( ~ ( q @ ( sK1 @ X1 ) )
| ( p @ ( sK1 @ X1 ) ) ) )
| ~ ( rel_s4 @ X1 @ ( sK1 @ X1 ) ) ) )
| ( $true
= ( r @ X1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
! [X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ X1 @ ( sK1 @ X1 ) ) ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $false
= ( ~ ( ~ ( ~ ( p @ ( sK1 @ X1 ) )
| ( q @ ( sK1 @ X1 ) ) )
| ~ ( ~ ( q @ ( sK1 @ X1 ) )
| ( p @ ( sK1 @ X1 ) ) ) ) ) )
| ( $true
= ( r @ X1 ) ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f166,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( ( ~ ( ~ ( p @ ( sK1 @ X1 ) )
| ( q @ ( sK1 @ X1 ) ) )
| ~ ( ~ ( q @ ( sK1 @ X1 ) )
| ( p @ ( sK1 @ X1 ) ) ) )
= $true )
| ( $true
= ( r @ X1 ) ) ),
inference(not_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( ( ~ ( ~ ( q @ ( sK1 @ X1 ) )
| ( p @ ( sK1 @ X1 ) ) ) )
= $true )
| ( $true
= ( ~ ( ~ ( p @ ( sK1 @ X1 ) )
| ( q @ ( sK1 @ X1 ) ) ) ) )
| ( $true
= ( r @ X1 ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( ~ ( q @ ( sK1 @ X1 ) )
| ( p @ ( sK1 @ X1 ) ) ) )
| ( $true
= ( ~ ( ~ ( p @ ( sK1 @ X1 ) )
| ( q @ ( sK1 @ X1 ) ) ) ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( p @ ( sK1 @ X1 ) ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( ~ ( p @ ( sK1 @ X1 ) )
| ( q @ ( sK1 @ X1 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X1: $i] :
( ( $false
= ( ~ ( q @ ( sK1 @ X1 ) ) ) )
| ( $true
= ( r @ X1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( ~ ( p @ ( sK1 @ X1 ) )
| ( q @ ( sK1 @ X1 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f171,plain,
! [X1: $i] :
( ( $true
= ( q @ ( sK1 @ X1 ) ) )
| ( $true
= ( r @ X1 ) )
| ( $true
= ( ~ ( ~ ( p @ ( sK1 @ X1 ) )
| ( q @ ( sK1 @ X1 ) ) ) ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( q @ ( sK1 @ X1 ) ) )
| ( $true
= ( r @ X1 ) )
| ( $false
= ( ~ ( p @ ( sK1 @ X1 ) )
| ( q @ ( sK1 @ X1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f174,plain,
! [X1: $i] :
( ( $true
= ( q @ ( sK1 @ X1 ) ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $false
= ( ~ ( p @ ( sK1 @ X1 ) ) ) )
| ( $true
= ( r @ X1 ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f175,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( p @ ( sK1 @ X1 ) ) )
| ( $true
= ( r @ X1 ) )
| ( $true
= ( q @ ( sK1 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X1: $i] :
( ( $false
= ( ~ ( p @ ( sK1 @ X1 ) )
| ( q @ ( sK1 @ X1 ) ) ) )
| ( $false
= ( p @ ( sK1 @ X1 ) ) )
| ( $true
= ( r @ X1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f177,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $false
= ( p @ ( sK1 @ X1 ) ) )
| ( $false
= ( q @ ( sK1 @ X1 ) ) )
| ( $true
= ( r @ X1 ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f180,plain,
! [X1: $i] :
( ( $true
= ( rel_s4 @ X1 @ ( sK1 @ X1 ) ) )
| ( $true
= ( r @ X1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f181,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f153]) ).
thf(f182,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ~ ( rel_s4 @ sK0 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f183,plain,
( $false
= ( ~ ( rel_s4 @ sK0 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f185,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f186,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f187,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X1: $i] :
( $true
= ( ~ ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) )
| ~ ( rel_s4 @ sK2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f188]) ).
thf(f190,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X1: $i] :
( ( $false
= ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f191]) ).
thf(f193,plain,
! [X1: $i] :
( ( $false
= ( ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) ) ) ) ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f195,plain,
! [X1: $i] :
( ( $true
= ( ~ ( p @ X1 )
| ( q @ X1 ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( ( q @ X1 )
= $true )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( ( q @ X1 )
= $true )
| ( $false
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f193]) ).
thf(f199,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( ( ~ ( q @ X1 ) )
= $true )
| ( $true
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( q @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f199]) ).
thf(f201,plain,
( $false
= ( ^ [Y0: $i] :
( ( r @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f185]) ).
thf(f202,plain,
( $false
= ( ( r @ sK3 )
| ~ ( rel_s4 @ sK2 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f203,plain,
( $false
= ( ~ ( rel_s4 @ sK2 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f202]) ).
thf(f204,plain,
( $false
= ( r @ sK3 ) ),
inference(or_proxy_clausification,[],[f202]) ).
thf(f205,plain,
( $true
= ( rel_s4 @ sK2 @ sK3 ) ),
inference(not_proxy_clausification,[],[f203]) ).
thf(f206,plain,
( $true
= ( rel_s4 @ sK0 @ sK2 ) ),
inference(not_proxy_clausification,[],[f183]) ).
thf(f207,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y2 @ Y1 )
& ( rel_s4 @ Y1 @ Y0 ) )
=> ( rel_s4 @ Y2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f208,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y2 @ Y1 )
& ( rel_s4 @ Y1 @ Y0 ) )
=> ( rel_s4 @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y1 @ Y0 )
& ( rel_s4 @ Y0 @ X1 ) )
=> ( rel_s4 @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f208]) ).
thf(f210,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y1 @ Y0 )
& ( rel_s4 @ Y0 @ X1 ) )
=> ( rel_s4 @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f209]) ).
thf(f211,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s4 @ Y0 @ X2 )
& ( rel_s4 @ X2 @ X1 ) )
=> ( rel_s4 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f210]) ).
thf(f212,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s4 @ Y0 @ X2 )
& ( rel_s4 @ X2 @ X1 ) )
=> ( rel_s4 @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f211]) ).
thf(f213,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s4 @ X3 @ X2 )
& ( rel_s4 @ X2 @ X1 ) )
=> ( rel_s4 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f212]) ).
thf(f214,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( rel_s4 @ X3 @ X2 )
& ( rel_s4 @ X2 @ X1 ) ) )
| ( $true
= ( rel_s4 @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f213]) ).
thf(f215,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_s4 @ X3 @ X1 ) )
| ( $false
= ( rel_s4 @ X2 @ X1 ) )
| ( $false
= ( rel_s4 @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f214]) ).
thf(f216,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f217,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f216]) ).
thf(f218,plain,
! [X1: $i] :
( $true
= ( rel_s4 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f217]) ).
thf(f389,plain,
! [X0: $i] :
( ( $false
= ( rel_s4 @ X0 @ sK2 ) )
| ( $true
= ( rel_s4 @ X0 @ sK3 ) )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f215,f205]) ).
thf(f408,plain,
! [X0: $i] :
( ( $true
= ( rel_s4 @ X0 @ sK3 ) )
| ( $false
= ( rel_s4 @ X0 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f389]) ).
thf(f427,plain,
( ( $false = $true )
| ( $false
= ( q @ ( sK1 @ sK3 ) ) )
| ( $true
= ( r @ sK3 ) )
| ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ( $false
= ( p @ ( sK1 @ sK3 ) ) ) ),
inference(constrained_superposition,[],[f408,f177]) ).
thf(f434,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ( $true
= ( q @ ( sK1 @ sK3 ) ) )
| ( $false = $true )
| ( $true
= ( r @ sK3 ) )
| ( ( p @ ( sK1 @ sK3 ) )
= $true ) ),
inference(constrained_superposition,[],[f175,f408]) ).
thf(f435,plain,
! [X0: $i,X1: $i] :
( ( $false = $true )
| ( $true
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ sK2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) ) ),
inference(constrained_superposition,[],[f215,f408]) ).
thf(f439,plain,
( ( $true
= ( r @ sK3 ) )
| ( $false
= ( q @ ( sK1 @ sK3 ) ) )
| ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ( $false
= ( p @ ( sK1 @ sK3 ) ) ) ),
inference(trivial_inequality_removal,[],[f427]) ).
thf(f445,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ sK2 ) )
| ( $true
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f435]) ).
thf(f447,plain,
( ( $true
= ( q @ ( sK1 @ sK3 ) ) )
| ( ( p @ ( sK1 @ sK3 ) )
= $true )
| ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ( $true
= ( r @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f434]) ).
thf(f449,plain,
( ( $false
= ( q @ ( sK1 @ sK3 ) ) )
| ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ( $false
= ( p @ ( sK1 @ sK3 ) ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f439,f204]) ).
thf(f450,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ( $false
= ( p @ ( sK1 @ sK3 ) ) )
| ( $false
= ( q @ ( sK1 @ sK3 ) ) ) ),
inference(trivial_inequality_removal,[],[f449]) ).
thf(f453,plain,
( ( $true
= ( q @ ( sK1 @ sK3 ) ) )
| ( ( p @ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( r @ sK3 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f447,f206]) ).
thf(f454,plain,
( ( $true
= ( q @ ( sK1 @ sK3 ) ) )
| ( $true
= ( r @ sK3 ) )
| ( ( p @ ( sK1 @ sK3 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f453]) ).
thf(f457,plain,
( ( $false
= ( q @ ( sK1 @ sK3 ) ) )
| ( $false = $true )
| ( $false
= ( p @ ( sK1 @ sK3 ) ) ) ),
inference(forward_demodulation,[],[f450,f206]) ).
thf(f458,plain,
( ( $false
= ( p @ ( sK1 @ sK3 ) ) )
| ( $false
= ( q @ ( sK1 @ sK3 ) ) ) ),
inference(trivial_inequality_removal,[],[f457]) ).
thf(f461,plain,
( ( ( p @ ( sK1 @ sK3 ) )
= $true )
| ( $false = $true )
| ( $true
= ( q @ ( sK1 @ sK3 ) ) ) ),
inference(forward_demodulation,[],[f454,f204]) ).
thf(f462,plain,
( ( ( p @ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( q @ ( sK1 @ sK3 ) ) ) ),
inference(trivial_inequality_removal,[],[f461]) ).
thf(f466,definition,
( spl4_20
<=> ( $false
= ( p @ ( sK1 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_20])],[avatar_definition]) ).
thf(f468,plain,
( ( $false
= ( p @ ( sK1 @ sK3 ) ) )
| ~ spl4_20 ),
inference(avatar_component_clause,[],[f466]) ).
thf(f470,definition,
( spl4_21
<=> ( $false
= ( q @ ( sK1 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_21])],[avatar_definition]) ).
thf(f472,plain,
( ( $false
= ( q @ ( sK1 @ sK3 ) ) )
| ~ spl4_21 ),
inference(avatar_component_clause,[],[f470]) ).
thf(f473,plain,
( spl4_20
| spl4_21 ),
inference(avatar_split_clause,[],[f458,f470,f466]) ).
thf(f476,definition,
( spl4_22
<=> ( ( p @ ( sK1 @ sK3 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_22])],[avatar_definition]) ).
thf(f477,plain,
( ( ( p @ ( sK1 @ sK3 ) )
!= $true )
| spl4_22 ),
inference(avatar_component_clause,[],[f476]) ).
thf(f478,plain,
( ( ( p @ ( sK1 @ sK3 ) )
= $true )
| ~ spl4_22 ),
inference(avatar_component_clause,[],[f476]) ).
thf(f480,definition,
( spl4_23
<=> ( $true
= ( q @ ( sK1 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_23])],[avatar_definition]) ).
thf(f482,plain,
( ( $true
= ( q @ ( sK1 @ sK3 ) ) )
| ~ spl4_23 ),
inference(avatar_component_clause,[],[f480]) ).
thf(f483,plain,
( spl4_22
| spl4_23 ),
inference(avatar_split_clause,[],[f462,f480,f476]) ).
thf(f485,plain,
( ( $false = $true )
| ~ spl4_20
| ~ spl4_22 ),
inference(forward_demodulation,[],[f478,f468]) ).
thf(f486,plain,
( $false
| ~ spl4_20
| ~ spl4_22 ),
inference(trivial_inequality_removal,[],[f485]) ).
thf(f487,plain,
( ~ spl4_20
| ~ spl4_22 ),
inference(avatar_contradiction_clause,[],[f486]) ).
thf(f599,plain,
! [X0: $i] :
( ( $true
= ( rel_s4 @ X0 @ ( sK1 @ sK3 ) ) )
| ( $false
= ( rel_s4 @ sK0 @ sK3 ) )
| ( $false = $true )
| ( $false
= ( rel_s4 @ X0 @ sK2 ) )
| ( $true
= ( r @ sK3 ) ) ),
inference(constrained_superposition,[],[f445,f180]) ).
thf(f628,plain,
! [X0: $i] :
( ( $false
= ( rel_s4 @ X0 @ sK2 ) )
| ( $false
= ( rel_s4 @ sK0 @ sK3 ) )
| ( $true
= ( rel_s4 @ X0 @ ( sK1 @ sK3 ) ) )
| ( $true
= ( r @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f599]) ).
thf(f646,plain,
! [X0: $i] :
( ( $false = $true )
| ( $true
= ( rel_s4 @ X0 @ ( sK1 @ sK3 ) ) )
| ( $false
= ( rel_s4 @ sK0 @ sK3 ) )
| ( $false
= ( rel_s4 @ X0 @ sK2 ) ) ),
inference(forward_demodulation,[],[f628,f204]) ).
thf(f647,plain,
! [X0: $i] :
( ( $true
= ( rel_s4 @ X0 @ ( sK1 @ sK3 ) ) )
| ( $false
= ( rel_s4 @ sK0 @ sK3 ) )
| ( $false
= ( rel_s4 @ X0 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f646]) ).
thf(f649,definition,
( spl4_24
<=> ( $false
= ( rel_s4 @ sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_24])],[avatar_definition]) ).
thf(f651,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK3 ) )
| ~ spl4_24 ),
inference(avatar_component_clause,[],[f649]) ).
thf(f653,definition,
( spl4_25
<=> ! [X0: $i] :
( ( $false
= ( rel_s4 @ X0 @ sK2 ) )
| ( $true
= ( rel_s4 @ X0 @ ( sK1 @ sK3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_25])],[avatar_definition]) ).
thf(f654,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s4 @ X0 @ ( sK1 @ sK3 ) ) )
| ( $false
= ( rel_s4 @ X0 @ sK2 ) ) )
| ~ spl4_25 ),
inference(avatar_component_clause,[],[f653]) ).
thf(f656,plain,
( spl4_25
| spl4_24 ),
inference(avatar_split_clause,[],[f647,f649,f653]) ).
thf(f660,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ( $false = $true )
| ~ spl4_24 ),
inference(constrained_superposition,[],[f651,f408]) ).
thf(f672,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ~ spl4_24 ),
inference(trivial_inequality_removal,[],[f660]) ).
thf(f682,plain,
( ( $false = $true )
| ~ spl4_24 ),
inference(forward_demodulation,[],[f672,f206]) ).
thf(f683,plain,
( $false
| ~ spl4_24 ),
inference(trivial_inequality_removal,[],[f682]) ).
thf(f684,plain,
~ spl4_24,
inference(avatar_contradiction_clause,[],[f683]) ).
thf(f697,plain,
( ( $false
= ( rel_s4 @ sK2 @ sK2 ) )
| ( $false = $true )
| ( ( p @ ( sK1 @ sK3 ) )
= $true )
| ( $false
= ( q @ ( sK1 @ sK3 ) ) )
| ~ spl4_25 ),
inference(constrained_superposition,[],[f654,f200]) ).
thf(f706,plain,
( ( $true
= ( q @ ( sK1 @ sK3 ) ) )
| ( $false
= ( p @ ( sK1 @ sK3 ) ) )
| ( $false
= ( rel_s4 @ sK2 @ sK2 ) )
| ( $false = $true )
| ~ spl4_25 ),
inference(constrained_superposition,[],[f197,f654]) ).
thf(f712,plain,
( ( $false
= ( q @ ( sK1 @ sK3 ) ) )
| ( $false
= ( rel_s4 @ sK2 @ sK2 ) )
| ( ( p @ ( sK1 @ sK3 ) )
= $true )
| ~ spl4_25 ),
inference(trivial_inequality_removal,[],[f697]) ).
thf(f721,plain,
( ( $false
= ( rel_s4 @ sK2 @ sK2 ) )
| ( $false
= ( p @ ( sK1 @ sK3 ) ) )
| ( $true
= ( q @ ( sK1 @ sK3 ) ) )
| ~ spl4_25 ),
inference(trivial_inequality_removal,[],[f706]) ).
thf(f731,plain,
( ( $false
= ( p @ ( sK1 @ sK3 ) ) )
| ( $true
= ( q @ ( sK1 @ sK3 ) ) )
| ( $false = $true )
| ~ spl4_25 ),
inference(forward_demodulation,[],[f721,f218]) ).
thf(f732,plain,
( ( $false
= ( p @ ( sK1 @ sK3 ) ) )
| ( $true
= ( q @ ( sK1 @ sK3 ) ) )
| ~ spl4_25 ),
inference(trivial_inequality_removal,[],[f731]) ).
thf(f754,plain,
( ( $false
= ( p @ ( sK1 @ sK3 ) ) )
| ( $false = $true )
| ~ spl4_21
| ~ spl4_25 ),
inference(forward_demodulation,[],[f732,f472]) ).
thf(f755,plain,
( ( $false
= ( p @ ( sK1 @ sK3 ) ) )
| ~ spl4_21
| ~ spl4_25 ),
inference(trivial_inequality_removal,[],[f754]) ).
thf(f770,plain,
( ( $false = $true )
| ~ spl4_21
| ~ spl4_22
| ~ spl4_25 ),
inference(forward_demodulation,[],[f755,f478]) ).
thf(f771,plain,
( $false
| ~ spl4_21
| ~ spl4_22
| ~ spl4_25 ),
inference(trivial_inequality_removal,[],[f770]) ).
thf(f772,plain,
( ~ spl4_21
| ~ spl4_22
| ~ spl4_25 ),
inference(avatar_contradiction_clause,[],[f771]) ).
thf(f783,plain,
( ( $false
= ( q @ ( sK1 @ sK3 ) ) )
| ( $false
= ( rel_s4 @ sK2 @ sK2 ) )
| spl4_22
| ~ spl4_25 ),
inference(forward_subsumption_resolution,[],[f712,f477]) ).
thf(f785,plain,
( ( $false = $true )
| ( $false
= ( rel_s4 @ sK2 @ sK2 ) )
| spl4_22
| ~ spl4_23
| ~ spl4_25 ),
inference(forward_demodulation,[],[f783,f482]) ).
thf(f786,plain,
( ( $false
= ( rel_s4 @ sK2 @ sK2 ) )
| spl4_22
| ~ spl4_23
| ~ spl4_25 ),
inference(trivial_inequality_removal,[],[f785]) ).
thf(f790,plain,
( ( $false = $true )
| spl4_22
| ~ spl4_23
| ~ spl4_25 ),
inference(forward_demodulation,[],[f786,f218]) ).
thf(f791,plain,
( $false
| spl4_22
| ~ spl4_23
| ~ spl4_25 ),
inference(trivial_inequality_removal,[],[f790]) ).
thf(f792,plain,
( spl4_22
| ~ spl4_23
| ~ spl4_25 ),
inference(avatar_contradiction_clause,[],[f791]) ).
cnf(s18,plain,
( spl4_20
| spl4_21 ),
inference(sat_conversion,[],[f473]) ).
cnf(s20,plain,
( spl4_22
| spl4_23 ),
inference(sat_conversion,[],[f483]) ).
cnf(s22,plain,
( ~ spl4_20
| ~ spl4_22 ),
inference(sat_conversion,[],[f487]) ).
cnf(s24,plain,
( spl4_24
| spl4_25 ),
inference(sat_conversion,[],[f656]) ).
cnf(s28,plain,
~ spl4_24,
inference(sat_conversion,[],[f684]) ).
cnf(s34,plain,
( ~ spl4_21
| ~ spl4_22
| ~ spl4_25 ),
inference(sat_conversion,[],[f772]) ).
cnf(s36,plain,
( spl4_22
| ~ spl4_23
| ~ spl4_25 ),
inference(sat_conversion,[],[f792]) ).
cnf(s37,plain,
spl4_25,
inference(rat,[],[s24,s28]) ).
cnf(s38,plain,
spl4_22,
inference(rat,[],[s20,s36,s37]) ).
cnf(s39,plain,
~ spl4_21,
inference(rat,[],[s34,s37,s38]) ).
cnf(s40,plain,
~ spl4_20,
inference(rat,[],[s22,s38]) ).
cnf(s41,plain,
$false,
inference(rat,[],[s18,s39,s40]) ).
thf(f793,plain,
$false,
inference(avatar_sat_refutation,[],[s41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO437^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n017.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:47:07 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.31 % (594598)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.31 % (594614)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2606606481:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.31 % (594620)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.31 % (594620)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.23/0.31 % (594615)lrs+10_16_si=on:nwc=1.5:random_seed=1220136052:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.31 % (594617)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=500692132:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.23/0.31 % (594616)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1281943442:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.31 % (594620)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2305339155:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.31 % (594619)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=877196952:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.31 % (594618)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=999043974:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.31 % (594616)Instruction limit reached!
% 0.23/0.31 % (594616)------------------------------
% 0.23/0.31 % (594616)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (594616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (594616)CaDiCaL version: 2.1.3
% 0.23/0.31 % (594616)Termination reason: Instruction limit
% 0.23/0.31 % (594616)Termination phase: Preprocessing 1
% 0.23/0.31 % (594616)Time elapsed: 0.002 s
% 0.23/0.31 % (594616)Peak memory usage: 10 MB
% 0.23/0.31 % (594616)Instructions burned: 4 (million)
% 0.23/0.31 % (594614) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-594598-594614"...
% 0.23/0.31 % (594614)...printing done.
% 0.23/0.31 % (594615)Instruction limit reached!
% 0.23/0.31 % (594615)------------------------------
% 0.23/0.31 % (594615)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (594615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (594615)CaDiCaL version: 2.1.3
% 0.23/0.31 % (594615)Termination reason: Instruction limit
% 0.23/0.31 % (594615)Termination phase: Saturation
% 0.23/0.31 % (594615)Time elapsed: 0.009 s
% 0.23/0.31 % (594615)Peak memory usage: 12 MB
% 0.23/0.31 % (594615)Instructions burned: 19 (million)
% 0.23/0.31 % (594614)Refutation found. Thanks to Tanya!
% 0.23/0.31 % SZS status Theorem for theBenchmark
% 0.23/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.31 % (594614)------------------------------
% 0.23/0.31 % (594614)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (594614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (594614)CaDiCaL version: 2.1.3
% 0.23/0.31 % (594614)Termination reason: Refutation
% 0.23/0.31 % (594614)Time elapsed: 0.015 s
% 0.23/0.31 % (594614)Peak memory usage: 13 MB
% 0.23/0.31 % (594614)Instructions burned: 53 (million)
% 0.23/0.31 % (594598)Success in time 0.051 s
% 0.23/0.31 % Vampire exiting
%------------------------------------------------------------------------------